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Stabilizing Sets for Linear Time-Invariant Continuous-Time Plants

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Analytical Design of PID Controllers

Abstract

In this chapter, we develop algorithms and procedures for the computation of the complete stabilizing set of PID controllers for continuous-time systems based on signature methods for root distribution determination. First, we present some basic results for the computation of stabilizing sets. Second, we provide justification and background for the computation of stabilizing sets. Then, we describe the procedure to compute the stabilizing set for LTI systems with P, PI, and PID controllers, and first-order controllers without delay. Finally, we present the computation of the PID stabilizing set which assigns closed-loop poles with real parts less than \(-\sigma \), for prescribed \(\sigma \).

Sections 2.1, 2.2 and 2.3 are reproduced from S. P. Bhattacharyya, A. Datta, L. H. Keel Linear System Theory: Structure, Robustness, and Optimization. Taylor & Francis LLC Books, with permission © 2008 Taylor & Francis LLC Books.

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Authors and Affiliations

  1. McAllen Higher Education Center, Texas A&M University, Mcallen, TX, USA

    Iván D. Díaz-Rodríguez

  2. Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA

    Sangjin Han & Shankar P. Bhattacharyya

Authors
  1. Iván D. Díaz-Rodríguez
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  2. Sangjin Han
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  3. Shankar P. Bhattacharyya
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Corresponding author

Correspondence to Sangjin Han .

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Díaz-Rodríguez, I.D., Han, S., Bhattacharyya, S.P. (2019). Stabilizing Sets for Linear Time-Invariant Continuous-Time Plants. In: Analytical Design of PID Controllers. Springer, Cham. https://doi.org/10.1007/978-3-030-18228-1_2

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